厄米对称多项式与CR复杂性
Hermitian symmetric polynomials and CR complexity
摘要：
利用Hermitian型的性质研究CR几何中的几个自然问题。对于每一个厄米对称多项式，我们指定一个厄米形式。我们研究了两个厄米特形式的签名对在多项式乘积下的行为。我们表明，除了三个平凡的情况下，每一个签名对可以从两个不定形式的产品。我们提供了几个新的应用程序的复杂性理论的有理映射之间的超二次曲面，包括一个稳定性结果的存在性的非平凡的有理映射从一个球到一个超二次曲面与一个给定的签名对。
英文摘要：
Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the polynomial product. We show, except for three trivial cases, that every signature pair can be obtained from the product of two indefinite forms. We provide several new applications to the complexity theory of rational mappings between hyperquadrics, including a stability result about the existence of non-trivial rational mappings from a sphere to a hyperquadric with a given signature pair.
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